(A): The error in Newton's formula of velocity of sound in air was 16%.
(R): The experimental value of velocity of sound in air at `0^(@)C` is 331m/s

Options

A. Both 'A' and 'R' are true and 'R' is the correct, explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. A' is true and 'R' is false
D. Both 'A' and 'R' are false

Answer

To solve the assertion-reason question, we need to analyze both the assertion and the reason provided in the question.

### Step 1: Analyze the Assertion
The assertion states: "The error in Newton's formula of velocity of sound in air was 16%."

- Newton's formula for the velocity of sound in air is given by:
\[ v = \sqrt{\frac{P}{\rho}} \]
where \(P\) is the pressure and \(\rho\) is the density of air.
- However, Newton assumed that sound travels through air as an isothermal process, which is not entirely accurate. The actual process is adiabatic.
- The approximate value of the velocity of sound calculated using Newton's formula is around 280 m/s.
- The accepted experimental value of the velocity of sound in air at \(0^\circ C\) is approximately 331 m/s.
- The percentage error can be calculated as:
\[ \text{Percentage Error} = \left( \frac{\text{Experimental Value} - \text{Newton's Value}}{\text{Experimental Value}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Error} = \left( \frac{331 - 280}{331} \right) \times 100 \approx 15.4\% \]
- This rounds to approximately 16%, confirming that the assertion is true.

### Step 2: Analyze the Reason
The reason states: "The experimental value of velocity of sound in air at \(0^\circ C\) is 331 m/s."

- This statement is a factual claim about the velocity of sound in air at \(0^\circ C\).
- The accepted experimental value of the velocity of sound in air at this temperature is indeed around 331 m/s, which makes the reason true.

### Step 3: Determine the Relationship
Now we need to determine if the reason correctly explains the assertion.

- The assertion is true because of the error in Newton's formula, which was due to the assumption of isothermal conditions.
- The reason is also true, but it does not directly explain why the error in Newton's formula is 16%. The error arises from the incorrect assumption about the nature of sound propagation, not merely from the value of sound velocity.

### Conclusion
Both the assertion and the reason are true, but the reason is not the correct explanation of the assertion.

### Final Answer
Both assertion and reason are true, but reason is not the correct explanation of assertion.

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